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Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
What is the approximate shape of the distribution of the sample means?
The approximate shape of the distribution of sample means is typically normal due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the shape of the population distribution. This normality holds true especially when the sample size is sufficiently large (usually n ≥ 30). The mean of this distribution will be equal to the population mean, and its standard deviation will be the population standard deviation divided by the square root of the sample size, known as the standard error.
In a standard normal distribution 95 of the data is within plus - standard deviations of the mean.?
In a standard normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ). This means that if you take the mean and add or subtract two times the standard deviation, you capture the vast majority of the data points. This property is a key aspect of the empirical rule, which describes how data is spread in a normal distribution.
What is the probability that x is within one standard deviation of its mean?
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This means that if x is a random variable that follows a normal distribution, there is about a 68% probability that x will be within one standard deviation of its mean. For distributions that are not normal, the probability may vary and would need to be determined based on the specific characteristics of that distribution.
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
What is the distribution with an means of 0 and a standard deviation of 1?
It is called a standard normal distribution.
The distribution of sample means is not always a normal distribution Under what circumstances will the distribution of sample means not be normal?
The distribution of sample means will not be normal if the number of samples does not reach 30.
Do some normal probability distributions have different means and different standard deviations?
Yes. Normal (or Gaussian) distribution are parametric distributions and they are defined by two parameters: the mean and the variance (square of standard deviation). Each pair of these parameters gives rise to a different normal distribution. However, they can all be "re-parametrised" to the standard normal distribution using z-transformations. The standard normal distribution has mean 0 and variance 1.
When the population standard deviation is not known the sampling distribution is a?
If the samples are drawn frm a normal population, when the population standard deviation is unknown and estimated by the sample standard deviation, the sampling distribution of the sample means follow a t-distribution.
In a standard normal distribution 95 of the data is within plus - standard deviations of the mean.?
In a standard normal distribution, approximately 95% of the data falls within two standard deviations (±2σ) of the mean (μ). This means that if you take the mean and add or subtract two times the standard deviation, you capture the vast majority of the data points. This property is a key aspect of the empirical rule, which describes how data is spread in a normal distribution.
What does a negative kurtosis mean?
It means distribution is flater then [than] a normal distribution and if kurtosis is positive[,] then it means that distribution is sharper then [than] a normal distribution. Normal (bell shape) distribution has zero kurtosis.
What does normal mean in a science way?
In science, "normal" typically means something that is within expected parameters or conforms to a standard. For example, a "normal distribution" refers to a bell-shaped curve that represents the expected distribution of a set of data points.
What does probalility distribution mean?
In parametric statistical analysis we always have some probability distributions such as Normal, Binomial, Poisson uniform etc.In statistics we always work with data. So Probability distribution means "from which distribution the data are?
Is the distribution of sample means always a normal distribution If not why?
It need not be if: the number of samples is small; the elements within each sample, and the samples themselves are not selected independently.
How do you calculate standard deviation without a normal distribution?
You calculate standard deviation the same way as always. You find the mean, and then you sum the squares of the deviations of the samples from the means, divide by N-1, and then take the square root. This has nothing to do with whether you have a normal distribution or not. This is how you calculate sample standard deviation, where the mean is determined along with the standard deviation, and the N-1 factor represents the loss of a degree of freedom in doing so. If you knew the mean a priori, you could calculate standard deviation of the sample, and only use N, instead of N-1.
What happens in a normal distribution when the means are equal but the standard deviation changes?
The two distributions are symmetrical about the same point (the mean). The distribution where the sd is larger will be more flattened - with a lower peak and more spread out.
